Abstract

We compare reconstructions based on the radiative transport and diffusion equations in optical tomography for media of small sizes. While it is well known that the diffusion approximation is less accurate to describe light propagation in such media, it has not yet been shown how this inaccuracy affects the images obtained with model-based iterative image reconstructions schemes. Using synthetic nondifferential data we calculate the error in the reconstructed images of optical properties as functions of source modulation frequency, noise level in measurement, and diffusion extrapolation length. We observe that the differences between diffusion and transport reconstructions are large when high modulation frequencies and noise-free data are used in the reconstructions. When the noise in data reaches a certain level, approximately 12% in our simulations, the differences between diffusion- and transport-based reconstructions become almost indistinguishable. Given that state-of-the-art optical imaging systems operate at much lower noise levels, the benefits of transport-based reconstructions of small imaging domains can be realized with most of the currently available systems. However, transport-based reconstructions are considerably slower than diffusion-based reconstructions.

Relative errors in reconstructions as functions of extrapolation length. Left: reconstructions with noise-free data; Right: reconstructions with 12% noise in the data. Transport reconstructions are shown here just as a reference.

Relative errors in transport and diffusion reconstructions using data with different noise levels in the presence of a void. Left: reconstructions with scattering coefficient
μs=10cm−1;
Right: reconstructions with scattering coefficient
μs=15cm−1. Anisotropy factor g = 0 in both cases.